i m explaining it to make it little-bit easy.
with set size =n , no of subset =2^n
1.now [{}(null set also represent a vertex),{a}{b}{c}{d}{e}...........(also represent verteces as isolated veteces since they hav no common element )] , so, we have (n+1) verteces with 0 degree
2. [{a,b}{b,c}{c,d}{d,e}{e,f}{f,g}{g,h}{h,i}...............] these subsets are common to any set whose cardinality is greater than 2 to make path between them, since all connected as network of branch they will be treated as 1 component
so, total component will be (n+1){with zero degree component} +1{all vertices as subsets connected whose cardinality >=2} = n+2